• 제목/요약/키워드: Equilibrium function

검색결과 703건 처리시간 0.03초

준설토 유동해석을 위한 유한요소 수식화 (Numerical Formulation for Flow Analysis of Dredged Soil)

  • 신호성
    • 한국지반환경공학회 논문집
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    • 제15권3호
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    • pp.41-48
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    • 2014
  • 준설토에 대한 연구는 주로 준설토의 1차원 침강 및 자중압밀 특성을 파악하는 실험적 연구가 진행되었다. 하지만 양질의 준설지반 확보를 위한 효과적인 투기장의 설계와 배출수에 의한 환경오염을 최소화하기 위해서는 준설토의 투기에 의한 유동특성의 체계적인 연구가 필요하다. 본 연구에서는 준설토 투기장의 펌핑에 의한 토사의 유동 형상을 모사하기 위하여 준설토사를 단일상으로 가정하고 연속 방정식을 유도하여 좌표축에 따른 힘 평형 방정식을 유도하였다. 준설토장의 3차원 거동 해석을 위한 컴퓨터 연산 부하와 모델링 소요시간을 최적화하기 위하여, 토체의 깊이 방향으로 적분을 수행하는 깊이 적분 방법을 지배 방정식에 적용하여, 3차원적 지형조건을 고려할 수 있도록 하였다. 지배 방정식의 보간함수를 이용한 공간분할에서 Petrov-Galerkin 수식화 기법을 적용하였다. 일반화된 사다리꼴 법칙으로 시간적분을 수행하고 Newton의 반복과정을 이용할 수 있도록 근사화시켰다. 가중행렬은 DG과 CDG 기법을 적용하였으며, 준설토 유동해석에서 가중행렬에 따른 수치적인 안정성을 평가하기 위하여 사각형 기둥 슬럼프 시뮬레이션을 수행하였다. 수치기법에 대한 비교 분석 결과는 DG 기법을 적용한 SU/PG 수식화가 유사진동을 최소화시키는 가장 안정적인 수치해석결과를 보여주는 것으로 나타났다.

유한요소법의 정도수렴 (The Convergence of Accuracy Ratio in Finite Element Method)

  • 조순보
    • 한국공간구조학회논문집
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    • 제3권2호
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    • pp.85-90
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    • 2003
  • If we use a third order approximation for the displacement function of beam element in finite element methods, finite element solutions of beams yield nodal displacement values matching to beam theory results to have no connection with the number increasing of elements of beams. It is assumed that, as the member displacement value at beam nodes are correct, the calculation procedure of beam element stiffness matrix have no numerical errors. A the member forces are calculated by the equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$, the member forces at nodes of beams have errors in a moment and a shear magnitudes in the case of smaller number of element. The nodal displacement value of plate subject to the lateral load converge to the exact values according to the increase of the number of the element. So it is assumed that the procedures of plate element stiffness matrix calculations has a error in the fundamental assumptions. The beam methods for the high accuracy ratio solution Is also applied to the plate analysis. The method of reducing a error ratio of member forces and element stiffness matrix in the finite element methods is studied. Results of study were as follows. 1. The matrixes of EI[B] and [K] in the equations of M(x)=EI[B]{q} and M(x) = [K]{q}+{Q} of beams are same. 2. The equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$ for the member forces have a error ratio in a finite element method of uniformly loaded structures, so equilibrium node loads {Q} must be substituted in the equation of member forces as the numerical examples of this paper revealed.

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Process Modeling and Optimization Studies in Drying of Current Transformers

  • Bhattacharya, Subhendu;D'Melo, Dawid;Chaudhari, Lokesh;Sharma, Ram Avatar;Swain, Sarojini
    • Transactions on Electrical and Electronic Materials
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    • 제13권6호
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    • pp.273-277
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    • 2012
  • The vacuum drying process for drying of paper in current transformers was modeled with an aim to develop an understanding of the drying mechanism involved and also to predict the water collection rates. A molecular as well as macroscopic approach was adopted for the prediction of drying rate. Ficks law of diffusion was adopted for the prediction of drying rates at macroscopic levels. A steady state and dynamic mass transfer simulation was performed. The bulk diffusion coefficient was calculated using weight loss experiments. The accuracy of the solution was a strong function of the relation developed to determine the equilibrium moisture content. The actually observed diffusion constant was also important to predict the plant water removal rate. Thermo gravimetric studies helped in calculating the diffusion constant. In addition, simulation studies revealed the formation of perpetual moisture traps (loops) inside the CT. These loops can only be broken by changing the temperature or pressure of the system. The change in temperature or pressure changes the kinetic or potential energy of the effusing vapor resulting in breaking of the loop. The cycle was developed based on this mechanism. Additionally, simulation studies also revealed that the actual mechanism of moisture diffusion in CT's is by surface jumps initiated by surface diffusion balanced against the surrounding pressure. Every subsequent step in the cycle was to break such loops. The effect of change in drying time on the electrical properties of the insulation was also assessed. The measurement of capacitance at the rated voltage and one third of the rated voltage demonstrated that the capacitance change is within the acceptance limit. Hence, the new cycle does not affect the electrical performance of the CT.

유한요소법에 의한 이차원연속체의 구조해석 (Structural Analysis of Two-dimensional Continuum by Finite Element Method)

  • 이재영;고재군
    • 한국농공학회지
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    • 제22권2호
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    • pp.83-100
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    • 1980
  • This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.

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동적(動的) 구조(構造) 재설계(再說計)를 위한 비선형(非線形) 섭동법(攝動法) (Nonlinea Perturbation Method for Dynamic Structural Redesign)

  • 조규남
    • 대한조선학회지
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    • 제26권1호
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    • pp.39-45
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    • 1989
  • 선체구조물이나 해양구조물의 동적응답중 원치 않는 고유진동수와 고유진동형태를 가지게 되는 경우가 있으며, 이러한 구조물은 동적 구조 재설계가 필수적이다. 본 소고에서는 비감쇄 구조물의 고유진동수와 진동형태를 기진력에 의한 특정한 진동수와 공진하지 않도록 또는 구조물의 중요한 부분이 특정 진동형태의 최대치에 오지 않도록 구조물의 질량과 강성을 최적하게 변화시키는 방법에 대해 논의하고 있다, 이 방법은 기존의 방법에서 사용되는 모든 고유진동형태의 수식포함과 달리 구속된 고유진동형태만을 미지수로 수식중에 사용하여 불필요한 계산과정을 줄이고 있다. 동적 구조 재설계중 최적화 문제에 중점을 두었으며 목적함수로는 구조물의 최소의 변화와 또는 최소의 중량을 취하였고, 예제를 통하여 본 방법의 응용과 효율성이 입증되었다. 예제에서는 간단한 구조물을 다루었으나 본 방법은 상용 유한요소코드의 연계이용으로 각종 선체구조물과 해양구조물의 진동문제해결에 응용될 수 있음은 자명한 일이다.

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$CCl_4$속에서 Thioamides 와 Dimethyl Sulfoxide (DMSO) 사이의 수소 결합에 대한 연구 (Hydrogen Bonding between Thioamides and Dimethylsulfoxide (DMSO) in $CCl_4$)

  • 도영락;김선진;윤창주;최영상
    • 대한화학회지
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    • 제36권2호
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    • pp.185-190
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    • 1992
  • 사염화탄소 속에서 대단히 묽은 티오아미드 및 티오아미드-DMSO 용액의 $ν_{\alpha}$ + Amide II 조합띠에 대한 근적외선 스펙트럼을 $5^{\circ}C$$55^{\circ}C$ 사이에서 얻었다. 이 조합띠는 두 개의 Lorentzian-Gaussian product 함수로 분해되며, 각각은 단체 티오아미드 및 1 : 1 티오아미드-DMSO 복합체로 확인되었다. 티오아세트아미드(TA)와 DMSO 사이의 수소결합은 티오프로피온 아미드(TPA)와 DMSO 사이의 수소결합보다 약간 강하며 $CCl_4$ 속에서 TA-DMSO와 TPA-DMSO 1: 1 복합체에 대한 ${\Delta}H^{\circ}$는 각각 -15.3 kJ${\cdot}$$mol^{-1}$ 및 -14.2 kj${\cdot}$$mol^{-1}$이었다.

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DCOC를 이용한 철근 콘크리트보의 최소경비설계 (Minimum Cost Design of Reinforced Concrete Beam Using DCOC)

  • 조홍동;한상훈
    • 한국전산구조공학회논문집
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    • 제13권4호
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    • pp.417-425
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    • 2000
  • 본 연구에서는 이산성 연속형 최적성규준방법(DCOC)을 이용하여 직사각형 단면을 갖는 철근콘크리트 연속보의 최적설계 알고리즘을 유도하였고, 최적설계 프로그램을 개발하였다. 목적함수로서 건설경비는 콘크리트 경비, 철근 경비 그리고 거푸집 경비를 포함하였으며 이를 최소화하였다. 설계제약조건으로는 시방서상의 최대처짐제약, 휨 및 전단강도제약, 연성제약 그리고 설계변수에 대한 상·하한 제약을 고려하였다. 쿤-터커 필요조건을 이용하여 최적성 규준을 설계변수의 항으로 명시적으로 유도하였으며, 이때 설계변수로는 보의 유효깊이와 철근비를 취하였다. 구조물 자중의 영향을 실제 시스템의 평형방정식에서 고려하였다. 설계변수들의 개선을 위한 반복과정과 컴퓨터 프로그램을 개발하였으며, 수치예를 들어 개발된 기법의 적용성과 효율성을 보였다.

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Newmark 기반 변형해석에 의한 필댐의 내진저항성 연구 (A Study on the Seismic Resistance of Fill-dams by Newmark-type Deformation Analysis)

  • 박동순
    • 한국지진공학회논문집
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    • 제18권4호
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    • pp.161-170
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    • 2014
  • Newmark-type deformation analysis has rarely been done in Korea due to the popularity of simple pseudo-static limit equilibrium analysis and detailed time-history FE/FD dynamic analysis. However, the Korean seismic dam design code updated in 2011 prescribes Newmark-type deformation analysis as a major dynamic analysis method for the seismic evaluation of fill dams. In addition, a design PGA for dynamic analysis is significantly increased in the code. This paper aims to study the seismic evaluation of four existing large fill dams through advanced FEM/Newmark-type deformation analyses for the artificial earthquake time histories with the design PGA of 0.22g. Dynamic soil properties obtained from in-situ geo-physical surveys are applied as input parameters. For the FEM/Newmark analyses, sensitivity analyses are performed to study the effects of input PGA and $G_{max}$ of shell zone on the Newmark deformation. As a result, in terms of deformation, four fill dams are proved to be reasonably safe under the PGA of 0.22g with yield coefficients of 0.136 to 0.187, which are highly resistant for extreme events. Sensitivity analysis as a function of PGA shows that $PGA_{30cm}$ (a limiting PGA to cause the 30 cm of Newmark permanent displacement on the critical slip surface) is a good indicator for seismic safety check. CFRD shows a higher seismic resistance than ECRD. Another sensitivity analysis shows that $G_{max}$ per depth does not significantly affect the site response characteristics, however lower $G_{max}$ profile causes larger Newmark deformation. Through this study, it is proved that the amplification of ground motion within the sliding mass and the location of critical slip surface are the dominant factors governing permanent displacements.

이산시간 전압모드 CMOS 혼돈 발생회로의 특성해석 (Characteristic Analysis of the Discrete Time Voltage Mode CMOS Chaos Generative Circuit)

  • 송한정;곽계달
    • 전자공학회논문지SC
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    • 제37권3호
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    • pp.55-62
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    • 2000
  • 0.8㎛ single poly CMOS 집적회로로 구현된 이산시간 전압모드 혼돈 발생회로의 동작특성을 분석하였다. 회로내 비선형 함수 블록에 대한 선형근사식을 유도하여, 실험적으로 제작한 혼돈 발생회로의 해석이 가능하도록 하였다. 혼돈상태 판별의 주요 지표인, 입력변수에 따른 분기도를 구하였고 초기값 의존성을 보여 주는 리아프노프 지수도 계산하였다. 뿐만 아니라 상태조건, 즉 평형상태, 주기상태, 혼돈상태에 따라 나타나는 시간파형 및 상태천이관계 그리고 주파수특성을 보여주는 전력스펙트럼도 구하여 상호 연관성을 보였다. 한편 집적화 된 혼돈 발생회로를 ±2.5V 전원, 10㎑의 클럭으로 구동시켜 입력전압에 따른 분기도를 측정하였고, 상태조건에 따라 다르게 나타나는 시간파형의 측정과 이의 전력스펙트럼 분석도 실시하여 해석결과와 비교하였다.

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Partial Confinement Utilization for Rectangular Concrete Columns Subjected to Biaxial Bending and Axial Compression

  • Abd El Fattah, Ahmed M.;Rasheed, Hayder A.;Al-Rahmani, Ahmed H.
    • International Journal of Concrete Structures and Materials
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    • 제11권1호
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    • pp.135-149
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    • 2017
  • The prediction of the actual ultimate capacity of confined concrete columns requires partial confinement utilization under eccentric loading. This is attributed to the reduction in compression zone compared to columns under pure axial compression. Modern codes and standards are introducing the need to perform extreme event analysis under static loads. There has been a number of studies that focused on the analysis and testing of concentric columns. On the other hand, the augmentation of compressive strength due to partial confinement has not been treated before. The higher eccentricity causes smaller confined concrete region in compression yielding smaller increase in strength of concrete. Accordingly, the ultimate eccentric confined strength is gradually reduced from the fully confined value $f_{cc}$ (at zero eccentricity) to the unconfined value $f^{\prime}_c$ (at infinite eccentricity) as a function of the ratio of compression area to total area of each eccentricity. This approach is used to implement an adaptive Mander model for analyzing eccentrically loaded columns. Generalization of the 3D moment of area approach is implemented based on proportional loading, fiber model and the secant stiffness approach, in an incremental-iterative numerical procedure to achieve the equilibrium path of $P-{\varepsilon}$ and $M-{\varphi}$ response up to failure. This numerical analysis is adapted to assess the confining effect in rectangular columns confined with conventional lateral steel. This analysis is validated against experimental data found in the literature showing good correlation to the partial confinement model while rendering the full confinement treatment unsafe.